6.
Which of the following is an appropriate change to make on a bank’s balance sheet
when GAP is negative, spread is expected to remain unchanged and interest rates are
expected to rise?
According to the CGAP effect, when GAP, or CGAP, is positive the change in NII is positively
related to the change in interest rates. Thus, an FI would want its GAP to be positive when interest
rates are expected to rise.
a. Replace fixed-rate loans with rate-sensitive loans
Yes. This change will increase RSAs, which will increase GAP.
b. Replace marketable securities with fixed-rate loans
No. This change will decrease RSAs, which will decrease GAP.
c. Replace fixed-rate CDs with rate-sensitive CDs
No. This change will increase RSLs, which will decrease GAP.
d. Replace equity with demand deposits
No. This change will have no impact on either RSAs or RSLs. So, will have no impact on GAP.
e. Replace vault cash with marketable securities
Yes. This change will increase RSAs, which will increase GAP.
7.
If a bank manager was quite certain that interest rates were going to rise within the next six
months, how should the bank manager adjust the bank’s six-month repricing gap to take
advantage of this anticipated rise? What if the manger believed rates would fall in the next six
months.
When interest rates are expected to rise, a bank should set its repricing gap to a positive position.
In this case, as rates rise, interest income will rise by more than interest expense. The result is an
increase in net interest income. When interest rates are expected to fall, a bank should set its
repricing gap to a negative position. In this case, as rates fall, interest income will fall by less
than interest expense. The result is an increase in net interest income.
8.
Consider the following balance sheet positions for a financial institution:

Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million

Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million

Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million
a.
Calculate the repricing gap and the impact on net interest income of a 1 percent increase
in interest rates for each position.

Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.
Repricing gap = RSA - RSL = $200 - $100 million = +$100 million.
ΔNII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.
Repricing gap = RSA - RSL = $100 - $150 million = -$50 million.
ΔNII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.
Repricing gap = RSA - RSL = $150 - $140 million = +$10 million.
NII = ($10 million)(0.01) = +$0.1 million, or $100,000.
b.
Calculate the impact on net interest income on each of the above situations assuming a 1
percent decrease in interest rates.

ΔNII = ($100 million)(-0.01) = -$1.0 million, or -$1,000,000.

ΔNII = (-$50 million)(-0.01) = +$0.5 million, or $500,000.

ΔNII = ($10 million)(-0.01) = -$0.1 million, or -$100,000.
c.
What conclusion can you draw about the repricing model from these results?
The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap), while
the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the lowest interest
rate risk exposure since the absolute value of the repricing gap is the lowest, while the opposite is
true for the FI in part (1).
9.
Consider the following balance sheet for MMC Bancorp (in millions of dollars):
Assets
Liabilities
$ 6.25
1. Equity capital (fixed)
$25.00
2. Short-term consumer loans
62.50
(one-year maturity)
2. Demand deposits
3. Long-term consumer loans
31.25
(two-year maturity)
3. Passbook savings
4. Three-month T-bills
37.50
4. Three-month CDs
5. Six-month T-notes
43.75
5. Three-month banker’s
acceptances
25.00
6. Three-year T-bonds
75.00
6. Six-month commercial paper
7. One-year time deposits
25.00
8. 30-year, floating-rate
50.00
8. Two-year time deposits
50.00
6.25
$337.50
50.00
37.50
50.00
75.00
$337.50
a. Calculate the value of MMC’s rate-sensitive assets, rate sensitive liabilities, and repricing
gap over the next year.
Looking down the asset side of the balance sheet, we see the following one-year rate-sensitive
assets (RSA):
1. Short-term consumer loans: $62.50 million, which are repriced at the end of the year and just
make the one-year cutoff.
2. Three-month T-bills: $37.50 million, which are repriced on maturity (rollover) every three
months.
3. Six-month T-notes: $43.75 million, which are repriced on maturity (rollover) every six
months.
4. 30-year floating-rate mortgages: $50.00 million, which are repriced (i.e., the mortgage rate is
reset) every nine months. Thus, these long-term assets are RSA in the context of the repricing
model with a one-year repricing horizon.
Summing these four items produces one-year RSA of $193.75 million. The remaining $143.75
million is not rate sensitive over the one-year repricing horizon. A change in the level of interest
rates will not affect the interest revenue generated by these assets over the next year. The $6.25
million in the cash and due from category and the $6.25 million in premises are nonearning
assets. Although the $131.25 million in long-term consumer loans, three-year Treasury bonds,
and 10-year, fixed-rate mortgages generate interest revenue, the level of revenue generated will
not change over the next year since the interest rates on these assets are not expected to change
(i.e., they are fixed over the next year).
Looking down the liability side of the balance sheet, we see that the following liability items
clearly fit the one-year rate or repricing sensitivity test:
1.
Three-month CDs: $50 million, which mature in three months and are repriced on
rollover.
2.
Three-month bankers acceptances: $25 million, which mature in three months and are
repriced on rollover.
3.
Six-month commercial paper: $75 million, which mature and are repriced every six
months.
4.
One-year time deposits: $25 million, which are repriced at the end of the one-year gap
horizon.
Summing these four items produces one-year rate-sensitive liabilities (RSL) of $175 million. The
remaining $162.50 million is not rate sensitive over the one-year period. The $25 million in
equity capital and $50 million in demand deposits do not pay interest and are therefore classified
as nonpaying. The $37.50 million in passbook savings and $50 million in two-year time deposits
generate interest expense over the next year, but the level of the interest generated will not
change if the general level of interest rates change. Thus, we classify these items as fixed-rate
liabilities.
The four repriced liabilities ($50 + $25 + $75 + $25) sum to $175 million, and the four repriced
assets of $62.50 + $37.50 + $43.75 + $50 sum to $193.75 million. Given this, the cumulative
one-year repricing gap (CGAP) for the bank is:
CGAP = (One-year RSA) - (One-year RSL) = RSA - RSL = $193.75 million - $175 million =
$18.75 million
b. Calculate the expected change in the net interest income for the bank if interest rates rise by
1 percent on both RSAs and RSLs. If interest rates fall by 1 percent on both RSAs and
RSLs.
The CGAP would project the expected annual change in net interest income (NII) of the bank
is:
NII = CGAP x R
= ($18.75 million) x 0.01
= $187,500
Similarly, if interest rates fall equally for RSAs and RSLs, NII will fall by:
= ($18.75 million) x (-0.01)
= -$187,5000
c. Calculate the expected change in the net interest income for the bank if interest rates rise by
1.2 percent on RSAs and by 1 percent on RSLs. If interest rates fall by 1.2 percent on RSAs
and by 1 percent on RSLs.
The resulting change in NII is calculated as:
NII = [RSA x R ] - [RSL x R ]
= [$193.75 million x 1.2%] - [$175 million x 1.0%]
= $2.325 million - $1.75 million
= $575,000
RSA
RSL
12.
test?
Which of the following assets or liabilities fit the one-year rate or repricing sensitivity
3-month U.S. Treasury bills Yes
1-year U.S. Treasury notes Yes
20-year U.S. Treasury bonds No
20-year floating-rate corporate bonds with annual repricing Yes
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds Yes
9-month fixed-rate CDs
Yes
1-year fixed-rate CDs Yes
5-year floating-rate CDs with annual repricing
Yes
Common stock
No
No
Yes
14.
A bank manager is quite certain that interest rates are going to fall within the next six
months. How should the bank manager adjust the bank’s six-month repricing gap and spread to
take advantage of this anticipated rise? What if the manager believes rates will rise in the next
six months.
When interest rates are expected to fall, a bank should set its repricing gap to a negative position.
Further, the manager would want to increase the spread between the return on RSAs and RSLs.
In this case, as rates fall, interest income will fall by less than interest expense. The result is an
increase in net interest income. When interest rates are expected to rise, a bank should set its
repricing gap to a positive position. Again, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates rise, interest income will rise by
more than interest expense. The result is an increase in net interest income.
15.
Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):
Assets
Liabilities and Equity
Floating-rate mortgages
(currently 10% annually)
30-year fixed-rate loans
(currently 7% annually)
Equity $10
Total assets $100
a.
1-year time deposits
$50
(currently 6% annually)
3-year time deposits
$50
(currently 7% annually)
Total liabilities & equity
$70
$20
$100
What is WatchoverU’s expected net interest income at year-end?
Current expected interest income: $50m(0.10) + $50m(0.07) = $8.5m.
Expected interest expense:
$70m(0.06) + $20m(0.07) = $5.6m.
Expected net interest income:
$8.5m - $5.6m = $2.9m.
b.
What will net interest income be at year-end if interest rates rise by 2 percent?
After the 2 percent interest rate increase, net interest income declines to:
50(0.12) + 50(0.07) - 70(0.08) - 20(.07) = $9.5m - $7.0m = $2.5m, a decline of $0.4m.
c.
Using the cumulative repricing gap model, what is the expected net interest
income for a 2 percent increase in interest rates?
WatchoverU’s repricing or funding gap is $50m - $70m = -$20m. The change in net interest
income using the funding gap model is (-$20m)(0.02) = -$0.4m.
d. What will net interest income be at year-end if interest rates on RSAs increase by 2
percent but interest rates on RSLs increase by 1 percent? Is it reasonable for changes in
interest rates on RSAs and RSLs to differ? Why?
After the unequal rate increases, net interest income will be 50(0.12) + 50(0.07) - 70(0.07) 20(.07) = $9.5m - $6.3m = $3.2m, an increase of $0.3m. It is not uncommon for interest rates to
adjust in an unequal manner on RSAs versus RSLs. Interest rates often do not adjust solely
because of market pressures. In many cases, the changes are affected by decisions of
management. Thus, you can see the difference between this answer and the answer for part a.
16.
Use the following information about a hypothetical government security dealer named M.
P. Jorgan. Market yields are in parenthesis, and amounts are in millions.
Assets
Liabilities and Equity
Cash $10
Overnight repos
$170
1-month T-bills (7.05%)
75
Subordinated debt
3-month T-bills (7.25%)
75
7-year fixed rate (8.55%)
2-year T-notes (7.50%)
50
8-year T-notes (8.96%)
100
5-year munis (floating rate)
(8.20% reset every 6 months) 25 Equity 15
Total assets $335 Total liabilities & equity
$335
150
a.
What is the repricing gap if the planning period is 30 days? 3 months? 2 years?
Recall that cash is a non-interest-earning asset.
Repricing gap using a 30-day planning period = $75 - $170 = -$95 million.
Repricing gap using a 3-month planning period = ($75 + $75) - $170 = -$20 million.
Reprising gap using a 2-year planning period = ($75 + $75 + $50 + $25) - $170 = +$55 million.
b.
What is the impact over the next 30 days on net interest income if interest rates
increase 50 basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will decrease by $475,000.
ΔNII = CGAP(ΔR) = -$95m.(0.005) = -$0.475m.
If interest rates decrease by 75 basis points, net interest income will increase by $712,500. ΔNII
= CGAP(ΔR) = -$95m.(-0.0075) = $0.7125m.
c. The following one-year runoffs are expected: $10 million for two-year T-notes and $20
million for eight-year T-notes. What is the one-year repricing gap?
The repricing gap over the 1-year planning period = ($75m. + $75m. + $10m. + $20m. + $25m.)
- $170m. = +$35 million.
d.
If runoffs are considered, what is the effect on net interest income at year-end if
interest rates increase 50 basis points? Decrease 75 basis points?
If interest rates increase 50 basis points, net interest income will increase by $175,000. ΔNII =
CGAP(ΔR) = $35m.(0.005) = $0.175m.
If interest rates decrease 75 basis points, net interest income will decrease by $262,500. ΔNII =
CGAP(ΔR) = $35m.(-0.0075) = -$0.2625m.
18.
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$550,000
755,000
265,000
$1,570,000
Avg. Rate
7.75%
8.75
Liabilities/Equity
Rate sensitive $575,000
Fixed rate
605,000
Nonpaying
390,000
Total
$1,570,000
Avg. Rate
6.25%
7.50
Suppose interest rates fall such that the average yield on rate-sensitive assets decreases by
15 basis points and the average yield on rate-sensitive liabilities decreases by 5 basis
points.
a.
Calculate the bank’s CGAP, gap to total asset ratio, and gap ratio.
CGAP = $550,000 - $575,000 = -$25,000
Gap to total assets ratio = -$25,000/$1,570,000 = -1.59%
Gap ratio = $550,000/$575,000 = 0.957
b.
Assuming the bank does not change the composition of its balance sheet, calculate the resulting
change in the bank’s interest income, interest expense, and net interest income.
ΔII = $550,000(-0.0015) = -$825
ΔIE = $575,000(-0.0005) = -$287.50
ΔNII = -$825 – (-$287.50) = -$537.50
c.
The bank’s CGAP is negative and interest rates decreased, yet net interest income decreased.
Explain how the CGAP and spread effects influenced this decrease in net interest income.
The CGAP affect worked to increase net interest income. That is, the CGAP was negative while
interest rates decreased. Thus, interest income decreased by less than interest expense. The result
is an increase in NII. The spread effect, on the other hand, worked to decrease net interest
income. The spread decreased by 10 basis points. According to the spread affect, as spread
decreases, so does net interest income. In this case, the increase in NII due to the CGAP effect
was dominated by the decrease in NII due to the spread effect.
19.
The balance sheet of A. G. Fredwards, a government security dealer, is listed below. Market
yields are in parentheses, and amounts are in millions.
Assets
Liabilities and Equity
Cash $20
Overnight repos
$340
1-month T-bills (7.05%)
150
Subordinated debt
3-month T-bills (7.25%)
150
7-year fixed rate (8.55%)
2-year T-notes (7.50%)
100
8-year T-notes (8.96%)
200
5-year munis (floating rate)
(8.20% reset every 6 months) 50 Equity 30
Total assets $670 Total liabilities and equity $670
a.
300
What is the repricing gap if the planning period is 30 days? 3 month days? 2 years?
Repricing gap using a 30-day planning period = $150 - $340 = -$190 million.
Repricing gap using a 3-month planning period = ($150 + $150) - $340 = -$40 million.
Repricing gap using a 2-year planning period = ($150 + $150 + $100 + $50) - $340 = $110 million.
b.
What is the impact over the next three months on net interest income if interest rates on
RSAs increase 50 basis points and on RSLs increase 60 basis points?
ΔII = ($150m. + $150m.)(0.005) = $1.5m.
ΔIE = $340m.(0.006) = $2.04m.
ΔNII = $1.5m. – ($2.04m.) = -$0.54m.
c. What is the impact over the next two years on net interest income if interest rates on RSAs
increase 50 basis points and on RSLs increase 75 basis points?
ΔII = ($150m. + $150m. + $100 + $50)(0.005) = $2.25m.
ΔIE = $340m.(0.0075) = $2.04m.
ΔNII = $2.25m. – ($2.04m.) = $0.21m.
d.
Explain the difference in your answers to parts (b) and (c). Why is one answer a negative
change in NII, while the other is positive?
For the 3-month analysis, the CGAP affect worked to decrease net interest income. That is, the
CGAP was negative while interest rates increased. Thus, interest income increased by less than
interest expense. The result is a decrease in NII. For the 3-year analysis, the CGAP affect worked
to increase net interest income. That is, the CGAP was positive while interest rates increased.
Thus, interest income increased by more than interest expense. The result is an increase in NII.
20.
A bank has the following balance sheet:
Assets
Rate sensitive
Fixed rate
Nonearning
Total
$225,000
550,000
120,000
$895,000
Avg. Rate
6.35%
7.55
Liabilities/Equity
Rate sensitive $300,000
Fixed rate
505,000
Nonpaying
90,000
Total
$895,000
Avg. Rate
4.25%
6.15
Suppose interest rates rise such that the average yield on rate-sensitive assets increases by
45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis
points.
Calculate the bank’s repricing GAP.
a.
Repricing GAP = $225,000 - $300,000 = -$75,000
b.
Assuming the bank does not change the composition of its balance sheet, calculate the net
interest income for the bank before and after the interest rate changes. What is the resulting
change in net interest income?
NII = ($225,000(0.0635) +$550,000(0.0755)) – ($300,000(0.0425) + $505,000(0.0615))
= $55,812.50 - $43,807.50 = $12,005
b
NII = ($225,000(0.0635 + 0.0045) +$550,000(0.0755)) – ($300,000(0.0425 + 0.0035) +
$505,000(0.0615)) = $56,825 - $44,857.50 = $11,967.50
a
ΔNII = $11,967.50 - $12,005 = -$37.50
c.
Explain how the CGAP and spread effects influenced this increase in net interest income.
The CGAP affect worked to decrease net interest income. That is, the CGAP was negative while
interest rates increased. Thus, interest income increased by less than interest expense. The result
is a decrease in NII. In contrast, the spread effect worked to increase net interest income. The
spread increased by 10 basis points. According to the spread affect, as spread increases, so does
net interest income. However, in this case, the increase in NII due to the spread effect was
dominated by the decrease in NII due to the CGAP effect.